Para un ángulo $x$ determine $\mathrm{sen}(2x),\cos (2x)y\tan (2x)$. sabiendo que $\tan x=-\frac{7}{8}$ y $\cos x>0$.

Step 1 ：We are given that $\tan (x)=-\frac{7}{8}$ and $\cos (x)>0$.

Step 2 ：From the given, we can find the values of $\sin (x)$ and $\cos (x)$ using the Pythagorean identity ${\sin }^2(x)+{\cos }^2(x)=1$.

Step 3 ：Since $\cos (x)>0$ and $\tan (x)<0$, we know that $\sin (x)<0$ (because in the unit circle, cosine is positive in the first and fourth quadrants, and tangent is negative in the fourth quadrant, so x must be in the fourth quadrant where sine is negative).

Step 4 ：After finding $\sin (x)$ and $\cos (x)$, we can use the double angle formulas to find $\sin (2x)$, $\cos (2x)$ and $\tan (2x)$:

Step 5 ：$\sin (2x)=2\sin (x)\cos (x)$

Step 6 ：$\cos (2x)={\cos }^2(x)-{\sin }^2(x)$

Step 7 ：$\tan (2x)=\frac{\sin (2x)}{\cos (2x)}$

Step 8 ：Let's calculate these step by step.

Step 9 ：$\tan (x)=-0.875$

Step 10 ：$\cos (x)=0.7525766947068778$

Step 11 ：$\sin (x)=0.658504607868518$

Step 12 ：$\sin (2x)=0.991150442477876$

Step 13 ：$\cos (2x)=0.13274336283185845$

Step 14 ：$\tan (2x)=7.466666666666663$

Step 15 ：Final Answer: The values of $\sin (2x)$, $\cos (2x)$ and $\tan (2x)$ are approximately $\boxed{{\displaystyle 0.991}}$, $\boxed{{\displaystyle 0.133}}$ and $\boxed{{\displaystyle 7.467}}$ respectively.